Measurement of point mobility and input energy of a beam under moment excitation

Moment excitation is often neglected within structural dynamic analysis since it is assumed that energy input to structures due to moment excitation is more important in the high frequency region. Also, difficulties in measuring the moment and resulting angular displacement has been a reason to exclude moment excitation from the analysis of vibrating structures. However, it has been shown that moment induced vibrational energy at low frequencies is important in the analysis when sources are close in proximity of discontinuities [1,2] and particularly if the translatory motion at a discontinuity is constrained [3,4]. Vibrational energy transmissions to machinery supporting structures subjected to multi-excitation systems were studied in [5,6]. However, difficulties occurred with the measurement of rotational response at lower frequencies and measurement of moment excitation. An investigation of moment excited beam structures using a T-and I-shape exciter configuration was of interest in [7,8]. The effects of loading due to moment exciter mass and transducer mass have been studied. It was found that two main bias errors when measuring moment mobility occurred. The authors suggested that the I-shape exciter configuration is the better choice when exciting structures by a applied moment. Moment excitation was applied to a simply supported aluminium plate in reference [9]. Two impact hammers to generate a force couple separated by a certain distance, acting parallel to each other and in opposite direction have been employed. Using this method, different force separation distances had to be taken into account when measuring a wide range of frequencies. The aim of this paper is to report a novel finite difference based measurement technique to measure the moment point mobility and the vibrational input energy to an experimental “infinite” rectangular beam. A first order finite difference approximation is used to approximate the angular displacement of the beam at the excitation location from recorded transverse acceleration signals. These signals were acquired by a pair of closely spaced accelerometers around the excitation location. The moment was induced by two opposite forces impacting the moment arms that were attached perpendicular to the beam.